Attaching another object to cloth simulation
You can define a Vertex Group and assign the tag mesh to it. This Vertex Group (&quot;Stiff&quot; in the example) you can add under Property Weights of the cloth sim and experiment with the values.
All in all, I got a good simulated shape but it's not suitable for animation because the collision detection is inaccurate and the tag appears sometimes on the other side or gets overlapped (clipping).
I removed a few edges of the tag, it's more low-poly than the rest. But I am not sure if that is a good idea (collision). You can also try and add some of the verts around the tag to the Stiff group for a better result.
The simulation is somewhat sensitive to the entered values. Small changes to Self Collision for example can have larger effects. If the value for Self Collision in my example is increased from 0.001m to 0.005m then the plane wraps around the tag and goes crazy.
Good luck ;-)